Simulation of Border Irrigation Using the two Numerical Schemes

Document Type : Research Paper

Authors

1 Assistant Professor, Water Engineering Department, University of Sari Agricultural Sciences and Natural Resources

2 M.S. Graduated from of Irrigation and Drainage, University of Sari Agricultural Sciences and Natural Resources

Abstract

Saint-venant equations constitute some of the basic relations that play important roles in different hydraulic studies, including the ones in surface irrigation. Throughout the present study, full hydrodynamic model of the flow was solved using finite difference method and dispersive explicit Lax (HD-LAX) as well as MacCormack (HD-MAC) schemes. In order to evaluate these two schemes, output with six measured data series were compared under different conditions. The results revealed that within an irrigation border, the prediction accuracy in both schemes increased by increase in inflow. The simulation accuracy of both schemes decreased by increase in length, width and slope of the border. The findings indicate that HD-LAX scheme with respective 0.9452 and 0.8366 coefficients of determination within the advance and recession flow phases’ simulation, and with -5.63 and 7.87 percent of the relative error are of more accuracy (in infiltrated water volume and runoff estimation) as compared with HD-MAC scheme.

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Main Subjects


Abbasi, F. (2013). Principles of Flow Surface Irrigation, (1sted.). Iranian National Committee on Irrigation and Drainage (IRNCID), 211. (In Farsi)
Abbasi, F., Mahmodian, S. M., and Feyen, J. (2003). Evaluation of varioussurface irrigation numerical simulation models. Journal of Irrigation and Drainage Engineering, 129, 208-213.
Abbasi, F. (1995). Use of the mathematical models for design of border irrigation systems. MS thesis, Tarbiat Modarres University, Tehran, Iran, 185. (In Farsi)
Aminizadeh, M. R., Liaghat, A., Mahmodian-Shoshtari, M., and Kouchakzadeh, S. (2007). An Explicit Scheme of Zero-Inertia Model Equations with Effectiveness ofWetted Perimeter for Furrow Irrigation Simulation. Journal of Agricultural Research. 6, 1-16. (In Farsi)
Baghlani, A. (2011). The confluenceof streamerosionandsediment transport simulations using finite volume method. Journal of Water Resources Engineering, 4, 1-12.(In Farsi)
Baghlani, A. (2009). Application of Surface Gradient Method in Flux-Vector Splitting forNumerical Solution of Shallow Water Equations. Journal of Water and Wastewater, 2, 81-89. (In Farsi)
Banti, M., Zissis, T. h., and Anastasiadou-Partheniou, E. (2011). Furrow Irrigation Advance Simulation Using a Surface–Subsurface Interaction Model. Journal of Irrigation and Drainage Engineering, 137, 304-14.
1. Finite Volume Method
Bautista, E. and Wallender, W. (1992). Hydrodynamic furrow irrigation model with specified space step. Journal of Irrigation and Drainage Engineering, 118, 450-465.
Bradford, S. and Katopodes, N. (2001). Finite Volume Model for Nonlevel Basin Irrigation. Journal of Irrigation and Drainage Engineering, 127, 216–223.
Chanson, H. (2004). Environmental Hydraulics of Open Channel Flows. Elsevier Butterworth-Heinemann, pp 485.
Clemmens, A., Strelkoff, T., and Playán, E. (2003). Field Verification of Two-Dimensional Surface Irrigation Model. Journal of Irrigation and Drainage Engineering, 129(6), 402–411.
Dong, Q., Xu, D., Zhang, S., Bai, M., and Li, Y. (2013). A Hybrid Coupled Model of Surface and Subsurface Flow for Surface Irrigation. Journal of Hydrology, 500, 62-74.
Ebrahimian, H. and Liaghat, M. (2011). A Field evaluation of various mathematical models for furrow and border irrigation systems. Journal of Soil and Water Research, 6(2), 91-101.
Elliott, R., and Walker, W. (1982). Field evaluation of furrow infiltration and advance functions [irrigation; Colorado]. Transactions of the ASAE, [American Society of Agricultural Engineers].
Esfandiari, M. and Maheshwari, B. L. (2001). Field evaluation of furrow irrigation models. Journal of Agricultural Engineering, 79, 459-479.
French, R. H. (1985). Open-Channel Hydraulics. Mc-Graw Hill, Inc. New York.
378 تحقیقات آب و خاک ایران، دورة 45 ، شمارة 4، زمستان 1393
Jaefarzadeh, M. R. and Alamatian, E. (2010). Numerical Analyses of Flow in TransitionsUsing Grid Adaptive Method. Journal of Iran-Water Resources Research, 5(3), 48-55. (In Farsi)
Jalalpoor, H. (2011). Presentation a numerical-mathematical model for implementing voronoi mesh in order to model dam break problem using unstructured finite volume method. MS thesis, islamic azad university, Tehran, Iran,pp 128. (In Farsi)
Katapodes, N. D. and Strelkoff, T. (1977). Hydrodynamics of Border Irrigation. Complete Model, Journal of the Irrigation and Drainage Engineering, 103, 309-324.
Kobus, H. (1988). Hydraulic modeling, German Association for Water Resources and Land Improvement Hamburg, Germany, 337.
Lin, G. F., Lai, J. S., and Guo, W. D. (2003). Finite volume Component-wise TVD Schemes for 2D ShallowWater Equations. Journal of Advances in Water Resources, 26, 861-873.
McClymont, D. J., Rain, S. R., and Smit, R. j. (1996). The Prediction of furrow irrigation performance using the surface irrigation model (SIRMOD). Irrigation Australia. Annual Conference of irrigation Association of Australian, Adelaide. 10.
Moravejalahkami, B., Mostafazadeh, F., Heidarpour, M., and Abbasi, F. (2009). Furrow Infiltration and Roughness Prediction for Different Furrow Inflow Hydrographs Using a Zero-Inertia Model with a Multilevel Calibration Approach. Journal of Biosystems Engineering, 103, 374-81.
Raghuwanshi, N., Saha, R., Mailapalli, D., and Upadhyaya, S. (2011). Infiltration Evaluation Strategy for Border Irrigation Management. Journal of Irrigation and Drainage Engineering, 137, 602–609.
Steinebach, G. and Weiner, R. (2012). Peer methods for the one-dimensional shallow waterequations with CWENO space discretization. Journal ofApplied Numerical Mathematics. 62(10), 1567-1578.
Strelkoff, T., Tamimi, A., and Clemmens, A. (2003). Two-Dimensional Basin Flow with Irregular Bottom Configuration. Journal of Irrigation and Drainage Engineering, 129, 391–401.
Strelkoff, T., Clemmens, A. J., El-Ansary, M., and Awad, M. (1999). Surface-Irrigation Evaluation models: Application to Level Basins in Egypt. Journal of Agricultural Engineers, 42, 1027-1036.
Soroush, F., Fenton, J. D., Mostafazadeh-Fard, B., Mousavi, S. F., and Abbasi, F. (2013). Simulation of Furrow Irrigation Using the Slow-Change/Slow-Flow Equation. Journal of Agricultural Water Management. 116, 160-74.
Walker, W. R. and Skogerboe, G. (1987). Surface Irrigation: Theory and Practice. Prentice-Hall, Englewood Cliffs, N.J.
Wallender, W. W. and Rayej, M. (1990). Shoting method for Saint-Venantequation of furrow irrigation. Journal of Irrigation and Drainage, 116(1), 114-122.
Ying, X., Wang, S., and Khan, A. (2003). Numerical Simulation of Flood Inundation due to Dam and Levee Breach. World Water and Environmental Resources Congress, 1-9.